I think the above poster's point is less about dealing with that misunderstanding and more against emptily restating the oppositions argument with the purpose of making them feel heard, WITHOUT expending any effort to actually understand their arguments.
Your point that people will restate their position if they don't feel like it's understood is valid. That doesn't remove the annoyance when someone SAYS the understand the point but clearly demonstrates that they don't.
Obviously both parts are very helpful: You should actually listen and consider the points being made to you, AND they should be shown that you have done this. Skipping either side is bad, but a lot of advice tells you to focus on the second, and not nearly enough tells you to do the first.
I mean, if we go all the way with this, I would say many times the person expressing an opinion may not actually realize (or be able to express) all the factors going in to their position.
If you seek to deeply understand their stance, they often start to understand it with more clarity as well, and sometimes you can then engage at the inflection point level and create a win-win.
Your point that people will restate their position if they don't feel like it's understood is valid. That doesn't remove the annoyance when someone SAYS the understand the point but clearly demonstrates that they don't.
Obviously both parts are very helpful: You should actually listen and consider the points being made to you, AND they should be shown that you have done this. Skipping either side is bad, but a lot of advice tells you to focus on the second, and not nearly enough tells you to do the first.